- -Q +Q d R Remember: Electric field caused by a capacitor (电容器) + There is also a small field outside the plates:

- d +Q -Q What is the potential difference across the capacitor? + Why is there a minus sign????

Definition of capacitance Capacitance C measures: - how much charge Q we must put on the plates - to achieve a certain potential difference ΔV. + - For parallel-plate capacitor:

Definition of capacitance Capacitance C measures: - how much charge Q we must put on the plates - to achieve a certain potential difference ΔV. + - For parallel-plate capacitor: A = area of plates d = separation of plates Units: the Farad (F)

Try to pull the plates apart… + -

Try to pull the plates apart… Electrical force on plate: + - Work done by you: This equals the change in potential energy of the system, ΔU.

I will now re-write this in a different way…

This is the electric field E between the plates. This is the change in volume (体积) of space between the plates.

Energy density in an electric field This is just another way of thinking about the potential energy U of the system of charges. It is not a ‘new’ energy.

Energy density in an electric field It is true for any electric field, not just in a capacitor! Electric fields contain energy. (Also momentum!)

I insert a metal slab between the plates I insert a metal slab between the plates. What is the potential difference now? -Q +Q s/3 s/3 +Q + - - -Q +

I insert a metal slab between the plates I insert a metal slab between the plates. What is the potential difference now? -Q +Q s/3 s/3 +Q + - - -Q + What happened to the capacitance?

I insert a dielectric between the plates I insert a dielectric between the plates. What is the potential difference now? +Q + - -Q

The dielectric constant εdepends on the material. Polarization of the dielectric reduces the net electric field between the plates. The dielectric constant εdepends on the material. +Q + - -Q

The dielectric constant εdepends on the material. It also reduces the potential difference between the plates. The dielectric constant εdepends on the material. +Q + - -Q

Summary Capacitance: Energy density in an electric field: Dielectrics reduce the electric field: